NDLI: Approximation Schemes for Functional Optimization Problems

Content Provider	Springer Nature Link
Author	Giulini, S. Sanguineti, M.
Copyright Year	2008
Abstract	Approximation schemes for functional optimization problems with admissible solutions dependent on a large number d of variables are investigated. Suboptimal solutions are considered, expressed as linear combinations of n-tuples from a basis set of simple computational units with adjustable parameters. Different choices of basis sets are compared, which allow one to obtain suboptimal solutions using a number n of basis functions that does not grow “fast” with the number d of variables in the admissible decision functions for a fixed desired accuracy. In these cases, one mitigates the “curse of dimensionality,” which often makes unfeasible traditional linear approximation techniques for functional optimization problems, when admissible solutions depend on a large number d of variables.
Starting Page	33
Ending Page	54
Page Count	22
File Format	PDF
ISSN	00223239
Journal	Journal of Optimization Theory and Applications
Volume Number	140
Issue Number	1
e-ISSN	15732878
Language	English
Publisher	Springer US
Publisher Date	2008-10-08
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Functional optimization Approximation schemes Complexity of admissible solutions Upper bounds on accuracy Curse of dimensionality Ritz method Extended Ritz method Operations Research/Decision Theory Engineering Applications of Mathematics Theory of Computation Optimization Calculus of Variations and Optimal Control; Optimization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization Management Science and Operations Research

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